This is a difficult thing to say with certainty. Within the military, mobility was greatly increased; before the Revolution, officers were required four generations of previous nobility and commoners were not allowed to go past the rank of Sergeant Major. This changed with the Revolution where officers would often be elected by the rules and merit eventually came to be an important part of promotion. This would continue to the Napoleonic Wars/French Empire where the military was very meritocratic although a brave soldier was more important than a tactical soldier.

Outside of the military, the Revolution was only helpful for the middle-class as they had the economic power to move beyond their "Third Estate" origins. They were able to send their children to schools which would feed the French military or civil service, which a person could become a noble if brave or effective. Most of this revolves around Paris rather than the rest of the country where the Revolution didn't have as much effect. So beyond Paris and the military, a peasant wouldn't have the same social mobility as he had before the Revolution.